# HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

*label*Mathematics

*timer*Asked: Aug 9th, 2015

**Question description**

Google Earth allows you to view many prominent buildings in 3d. Imagine that you are

the maths wiz at Google whose job it is to create a 3d image of our cube for Google Earth.

This means that you have to and coordinates of the corners of the square A;B;C;D visible

from the top, as well as the coordinates of the points A0;B0;C0;D0 at which four edges of

the Cube meet the ground. As indicated in the rst picture, A is supposed to be connected

to A0 by such an edge, and similarly for B and B0, C and C0, and D and D0.

You are new to this job and you are supposed to base your work on your predecessor's

work (who got fired yesterday). His notes are a terrible mess, but it is clear that he started

modelling the cube by letting the (

at) ground coincide with the xy-plane and having the

y-axis point West and the x-axis point North. His notes don't tell you where the origin of

his coordinate system is supposed to be, but wherever it may be, in this coordinate system

B = (26:3720; 35:3768; 13:1872), B0 = (24:9863; 31:7691; 0), D = (54:0957; 24:7282; 13:1872):

Your job also involves guring out how long the sides of the cube are; how long the four

segments AA0;BB0;CC0;DD0 are; how large the area of the quadrilateral A0;B0;C0;D0 is;

and, finally, what the volume of the part of the cube that sits above the ground is.